The Result

Genetic programming evolved analog computational circuits for squaring, cubing, square root, cube root, and logarithm as described in Chapter 47 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999). In addition to the above five computational circuits, a circuit for the Gaussian function is created in Chapter 51 using MOSFET semiconductor technology.

BBB604

Basis for Claim of Human-Competitiveness

The problem of designing analog computational circuits for specified mathematical functions is recognized as being exceedingly difficult. Dozens of computational circuits have been patented, including square root circuits (Newbold 1962; Schlatter 1973), logarithmic circuits (Green 1958; Platzer 1965; Gilbert 1991), and multiplier circuits (Gilbert 1979).

Referring to the eight criteria in chapter 1 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999) for establishing that an automatically created result is competitive with a human-produced result, the automatic synthesis of analog computational circuits for the squaring, cubing, square root, cube root, logarithm, and Gaussian functions satisfies the following three criteria:

(A) The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.

(D) The result is publishable in its own right as a new scientific result (independent of the fact that the result was mechanically created).

(G) The result solves a problem of indisputable difficulty in its field.

References

Gilbert, Barrie.. 1979. Multiplier Circuit. U.S. Patent 4,156,283. Filed October 3, 1977. Issued May 22, 1979.

Gilbert, Barrie. 1991. Logarithmic Amplifier. U.S. Patent 4,990,803. Filed March 27, 1989. Issued February 5, 1991.

Green, Milton. 1958. Logarithmic Converter Circuit. U.S. Patent 2,861,182. Filed June 16, 1953. Issued November 18, 1958.

Koza, John R., Bennett III, Forrest H, Andre, David, and Keane, Martin A. 1999a. Genetic Programming III: Darwinian Invention and Problem Solving. San Francisco, CA: Morgan Kaufmann.

Newbold, William F. 1962. Square Root Extracting Integrator. U.S. Patent 3,016,197. Filed September 15, 1958. Issued January 9, 1962.

Platzer, George E. 1965. Logarithmic Multiplier-Divider. U.S. Patent 3,197,626. Filed January 8, 1962. Issued July 27, 1965.

Schlatter, Gerald Lance. 1973. Analog Multiplier and Square Root Extractor Having a Plurality of Strain Gages Connected in a Bridge Circuit. U.S. Patent 3,732,406. Filed July 8, 1971. Issued May 8, 1973.

· The home page of Genetic Programming Inc. at www.genetic-programming.com.

· For information about the field of genetic programming and the field of genetic and evolutionary computation, visit www.genetic-programming.org

· The home page of John R. Koza at Genetic Programming Inc. (including online versions of most published papers) and the home page of John R. Koza at Stanford University

· For information about John Koza’s course on genetic algorithms and genetic programming at Stanford University

· Information about the 1992 book Genetic Programming: On the Programming of Computers by Means of Natural Selection, the 1994 book Genetic Programming II: Automatic Discovery of Reusable Programs, the 1999 book Genetic Programming III: Darwinian Invention and Problem Solving, and the 2003 book Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Click here to read chapter 1 of Genetic Programming IV book in PDF format.

· 3,440 published papers on genetic programming (as of November 28, 2003) in a searchable bibliography (with many on-line versions of papers) by over 880 authors maintained by William Langdon’s and Steven M. Gustafson.

· For information on the Genetic Programming and Evolvable Machines journal published by Kluwer Academic Publishers

· For information on the Genetic Programming book series from Kluwer Academic Publishers, see the Call For Book Proposals

· For information about the annual Genetic and Evolutionary Computation (GECCO) conference (which includes the annual GP conference) to be held on June 26–30, 2004 (Saturday – Wednesday) in Seattle and its sponsoring organization, the International Society for Genetic and Evolutionary Computation (ISGEC). For information about the annual Euro-Genetic-Programming Conference to be held on April 5-7, 2004 (Monday – Wednesday) at the University of Coimbra in Coimbra Portugal. For information about the 2003 and 2004 Genetic Programming Theory and Practice (GPTP) workshops held at the University of Michigan in Ann Arbor. For information about Asia-Pacific Workshop on Genetic Programming (ASPGP03) held in Canberra, Australia on December 8, 2003. For information about the annual NASA/DoD Conference on Evolvable Hardware Conference (EH) to be held on June 24-26 (Thursday-Saturday), 2004 in Seattle.

Last updated on December 28, 2003